Instructional Video
Khan Academy

Khan Academy: 3 D Vector Fields, Introduction

11th Standards
Vector fields can also be three-dimensional, though this can be a bit trickier to visualize.
Instructional Video
Khan Academy

Khan Academy: 3 D Vector Field Example

11th Standards
See an example of how you can start to understand how the formula for a three-dimensional vector field relates to the way it looks.
Instructional Video
Khan Academy

Khan Academy: 3 D Curl Intuition, Part 2

11th
Continuing the intuition for how three-dimensional curl represents rotation in three-dimensional fluid flow.
Instructional Video
Khan Academy

Khan Academy: 3 D Curl Formula, Part 2

11th
This finishes the demonstration of how to compute three-dimensional curl using a certain determinant.
Instructional Video
Khan Academy

Khan Academy: 3 D Curl Formula, Part 1

11th
How to compute a three-dimensional curl, imagined as a cross product of sorts.
Instructional Video
Khan Academy

Khan Academy: 3 D Curl Computation Example

11th
A worked example of a three-dimensional curl computation.
Instructional Video
Khan Academy

Khan Academy: 2 D Curl Nuance

11th
The meaning of positive curl in a fluid flow can sometimes look a bit different from the clear cut rotation-around-a-point examples discussed in previous videos.
Instructional Video
Khan Academy

Khan Academy: 2 D Curl Intuition

11th
A description of how vector fields relate to fluid rotation, laying the intuition for what the operation of curl represents.
Instructional Video
Khan Academy

Khan Academy: 2 D Curl Formula

11th Standards
Here we build up to the formula for computing the two-dimensional curl of a vector field, reasoning through what partial derivative information corresponds to fluid rotation.
Instructional Video
Khan Academy

Khan Academy: 2 D Curl Example

11th
A worked example of computing and interpreting two-dimensional curl.
Instructional Video
Khan Academy

Khan Academy: 3 D Divergence Theorem Intuition

11th
Intuition behind the Divergence Theorem in three dimensions.
Instructional Video
Khan Academy

Khan Academy: 3 D Curl Intuition, Part 1

11th
Here we start transitioning from the understanding of two-dimensional curl into an understanding of three-dimensional curl.